Epigenetic phenomena are defined as morpho-physiological changes not related to impairments of DNA sequence. The results of our study indicate that a pulsed non-mutagenic thermal stress inflicted on developing ova (pro-embryos) gives rise to positive transgenerational epigenetic changes in the life span of offspring. At that, this effect depends on heterozygosity by lgl-mutation inherited from mothers. In generation Fl, determination of higher survival trait occurs even at early stages of oogenesis. The most pronounced effect is observed when heating is applied to the cells at the earliest stages of pro-embryo development. This study is the first experimental work on modeling the transgenerational aftereffects of pre-zygotic (pro-embryo) stress on offspring survivability and longevity when tumor suppressor lgl is operating. The significance of the results with regard to human epigenetics is discussed.